Many applications in multi-rate digital signal processing require the analysis of input signals that are finite in length. Multi-rate filter banks provide an excellent and efficient means of analyzing input signals that are infinite in length, but have stumbled when the input signal is finite in length. Filter banks for signals finite in length have been extensively studied, and solutions to this problem include boundary filter design and signal extension techniques. Signal extension techniques are computationally simple, but generally result in an expansive filter bank (which may result in more sub-band coefficients than the original length of the input signal) and exhibit non-ideal behavior at the boundaries. Boundary filter design techniques are length-preservative, but have not guaranteed certain properties (e.g., frequency selectivity or number of vanishing moments) for a wide range of analysis filters (e.g., minimum phase filters).